具有三体相互作用海森堡自旋链模型的纠缠与几何失协

近年来有研究发现量子失协可以度量非纠缠的量子关联,而且非纠缠的量子关联在量子通信和量子计算中起到很重要的作用.研究了磁场,两种三体相互作用,各向异性参数,耦合常数,温度等参数对同时具有两种三体相互作用海森堡XXZ自旋链系统的量子纠缠,几何失协的影响以及与量子相变的关系.研究表明:量子纠缠和几何失协都可以清晰的表征本模型系统的量子相变现象; 随着XZX+YZY型三体相互作用的增加量子纠缠和几何失协即使在高温时也可达到最大值;几何失协比量子纠缠更全面地描述了量子关联; XZY-YZX型三体相互作用的增加对量子纠缠有抑制作用;XZY-YZX型三体相互作用在一定区域内的增加对几何失协有抑制作用,在另一区域的增加可使几何失协增大到一个稳定的非零值。增大磁场和自旋耦合常数,减小各向异性参数会使纠缠的临界温度变大; 调节自旋耦合常数可更有效的使量子纠缠和几何失协在高温时仍有一个较大的值.同时发现,在磁场 和各向异性参数 的区域两种量子关联都可以维持在最大值.     

海森堡自旋链的几何量子失协

本文采用Diosi、Gisin提出的非马尔科夫量子态扩散方法,系统地研究了处于非马尔科夫环境中海森堡自旋链模型的几何量子失协。首先通过非马尔科夫量子态扩散主方程计算出系统的约化密度矩阵。然后将约化密度矩阵带入量子失协公式中,从而实现了在数值上精确地模拟海森堡自旋链的几何量子失协。最后以最大纠缠态■作为系统的初始态,详细地讨论了系统中各种参数在海森堡自旋链几何量子失协中的作用。根据数值模拟结果显示:环境关联系数γ、参数J、参数α和参数η能从不同的程度上影响量子系统几何量子失协动力学的演化过程。当环境关联系数γ较小时,几何量子失协呈现出明显的上升趋势。表明非马尔科夫环境对系统的几何量子失协具有积极的作用。同时较大的参数J、参数α和参数η对系统的几何量子失协也有积极的作用。本文的研究对于增加系统的几何量子失协具有一定的作用和意义,为实验研究者在实际中提高几何量子失协提供了理论依据。     

非马尔科夫环境中各向异性海森堡自旋链的几何量子失协

本文主要在非马尔科夫环境中,在时变磁场和Dzyaloshinski—Moriya相互作用下,以最大纠缠态■作为信道,研究了具有各种参数的两比特海森堡XYZ模型的几何量子失协.通过在非马尔科夫环境中的量子态扩散方法模拟了系统的几何量子失协随时间的演化关系.根据数值模拟结果显示:环境关联系数γ、自旋耦合系数J和J_z、余弦磁场强度B、以及自旋—轨道相互作用都能影响系统几何量子失协的性质.当环境关联系数γ较小时,几何量子失协呈现出明显的上升趋势,可见非马尔科夫环境对系统的几何量子失协表现出积极的作用.同时较大的自旋耦合系数J和余弦磁场强度B对系统的几何量子失协也有积极的影响.     

Tavis-Cummings模型中的几何量子失协特性

采用几何量子失协的计算方法,通过改变两原子初始状态、腔内光子数和偶极-偶极相互作用强度,研究了Tavis-Cummings模型中的几何量子失协特性.结果表明:几何量子失协都是随时间周期性振荡的,选取适当的初态可以使两原子一直保持失协状态,增加腔内光子数和偶极相互作用对几何量子失协有积极的影响.     

具有三体相互作用自旋链的量子相干与量子纠缠

本文研究了具有两种三体相互作用的海森堡XXZ自旋链的量子相干与量子纠缠的特性。研究发现,量子相干性不会出现突然死亡现象且非零量子相干性存在的温度范围大于量子纠缠存在的温度范围,说明量子相干性相对于量子纠缠,具有更强的鲁棒性。在量子临界环境中,量子相干性可以表征本模型的量子相变现象。在铁磁情形中,无论外磁场是否为0,单独调控XZX+YZY三体相互作用对于减缓量子相干性的衰减速率与增大量子相干性存在的温度范围效果最好。在反铁磁情形中,外磁场为0时,XZX+YZY与XZY-YZX两种三体相互作用的协同作用可以显著增加量子相干性的最大值,并明显减缓其衰减速率。在铁磁情形与反铁磁情形中都发现当外磁场B <0时,量子相干性存在的温度范围更大,更有利于保存量子相干性。     

不同磁场环境下Heisenberg XXZ自旋链中的热量子失协

本文研究了不同磁场环境下一维Heisenberg XXZ自旋链中两量子比特的热量子失协特性. 在四种不同的磁场环境下: 1) B₁=B₂=0 (无磁场); 2) B₁≠0, B₂=0 (磁场只作用于其中一个量子比特); 3) B₁=B₂ (均匀磁场); 4) B₁=-B₂ (非均匀磁场), 对分别作用在每个量子比特上的磁场B₁和B₂对其量子关联的影响作了详细的讨论, 且数值计算和比较了其量子失协和量子纠缠的异同. 结果显示: 在有限温度下, 量子失协相比于量子纠缠更普遍, 且非均匀磁场相比于均匀磁场对量子失协和量子纠缠更有用, 更有利于量子通讯和量子信息处理过程.关键词：量子关联纠缠量子失协     

无相互作用原子之间的纠缠和量子失协

研究两个无相互作用的二能级原子分别与单模热光场相互作用时的纠缠和量子失协动力学,重点讨论原子运动和腔体热环境温度对纠缠和量子失协的影响。结果表明:受原子运动和场模结构参数的影响,两原子的纠缠和量子失协周期性地演化;在原子纠缠消失处仍存在量子失协。此外,通过控制腔体热环境温度和场模结构参数可以实现对纠缠和量子失协的调控,使其得以保持。     

具有三体相互作用的自旋链系统中的几何相位与量子相变

本文首先对具有三体相互作用的一维自旋链系统的哈密顿量进行了对角化．然后通过一个旋转操作求解了系统基态的几何相位,通过数值计算几何相位及其导数随外界参数的变化,考虑三体相互作用对几何相位以及量子相变的影响,结果表明几何相位可以很好的用来表征该系统中的量子相变,并且发现三体相互作用不但引起相变点平移,而且可以产生新的临界点．     

含三体相互作用的海森堡自旋链纠缠研究

研究了含三体相互作用的海森堡自旋链的能级和相应本征态的纠缠情况,详细分析了含有三个粒子的海森堡自旋链的纠缠,发现所有的纠缠态都为W态。给出三粒子海森堡自旋链在温度为零时的基态纠缠,发现反铁磁自旋链的基态不随各向异性、耦合强度等参数发生变化,铁磁自旋链的基态纠缠随各向异性因子和三自旋耦合项而改变。讨论了三比特自旋链在低温时的热纠缠,给出纠缠度表达式及其随温度、各向异性因子和耦合强度的变化关系。     

非马尔科夫环境中各向异性海森堡自旋链的量子失协

利用量子失协方法研究在非马尔科夫环境中具有时变磁场的两比特各向异性海森堡XYZ模型量子失协的动力学演化。海森堡XYZ系统的初始态为最大纠缠态 $left|psi_{A B}rightrangle=(1 / sqrt{2})(|11rangle+|00rangle)$ , 利用非马尔科夫量子态扩散方法解析求解非马尔科夫主方程, 得出系统的约化密度矩阵; 然后代入量子失协公式得出系统量子失协的演化动力学。讨论自旋耦合强度、环境关联系数γ和余弦磁场强度B对量子失协动力学的影响。研究发现: 当环境关联系数γ较小时, 系统的量子失协明显呈现上升趋势, 因此可以表明非马尔科夫环境具有增加系统量子失协的作用。同时较大的自旋耦合系数J和J_Z以及余弦磁场强度B也具有增加系统量子失协的作用。     

One-norm geometric quantum discord and critical point estimation in the XY spin chain

In contrast with entanglement and quantum discord (QD), we investigate the thermal quantum correlation in terms of Schatten one-norm geometric quantum discord (GQD) in the XY spin chain, and analyze their capabilities in detecting the critical point of quantum phase transition. We show that the one-norm GQD can reveal more properties about quantum correlation between two spins, especially for the long-range quantum correlation at finite temperature. Under the influences of site distance, anisotropy and temperature, one-norm GQD and its first derivative make it possible to detect the critical point efficiently for a general XY spin chain.     

Long-range quantum discord in critical spin systems

We show that quantum correlations as quantified by quantum discord can characterize quantum phase transitions by exhibiting nontrivial long-range decay as a function of distance in spin systems. This is rather different from the behavior of pairwise entanglement, which is typically short-ranged even in critical systems. In particular, we find a clear change in the decay rate of quantum discord as the system crosses a quantum critical point. We illustrate this phenomenon for first-order, second-order, and infinite-order quantum phase transitions, indicating that pairwise quantum discord is an appealing quantum correlation function for condensed matter systems.     

Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.     

Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state

We have investigated the effect of counter-rotating terms on the dynamics of entanglement and quantum discord between two identical atoms interacting with a lossy single mode cavity field for a system initially in a vacuum state. The counter-rotating terms are found to lead to steady states in the long-time limit which can have high quantum discord, but have no entanglement. The effect of cavity decay rate on this steady-state quantum discord has been also investigated, surprisingly, the increase in cavity decay rate is found to enhance the steady-state quantum discord.     

Quantum correlations support probabilistic pure state cloning

The probabilistic scheme for making two copies of two nonorthogonal pure states requires two auxiliary systems, one for copying and one for attempting to project onto the suitable subspace. The process is performed by means of a unitary-reduction scheme which allows having a success probability of cloning different from zero. The scheme becomes optimal when the probability of success is maximized. In this case, a bipartite state remains as a free degree which does not affect the probability. We find bipartite states for which the unitarity does not introduce entanglement, but does introduce quantum discord between some involved subsystems.     

Correlation dynamics of qubit-qutrit systems in a classical dephasing environment

We study the time evolution of classical and quantum correlations for hybrid qubit-qutrit systems in independent and common dephasing environments. Our discussion involves a comparative analysis of the Markovian dynamics of negativity, quantum discord, geometric measure of quantum discord and classical correlation. For the case of independent environments, we have demonstrated the phenomenon of sudden transition between classical and quantum decoherence for qubit-qutrit states. In the common environment case, we have shown that dynamics of quantum and geometric discords might be completely independent of each other for a certain time interval, although they tend to be eventually in accord.     

Quantum correlations in non-Markovian environments

We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states.     

Collapse–revival of quantum discord and entanglement

In this paper the correlations dynamics of two atoms in the case of a micromaser-type system is investigated. Our results predict certain quasi-periodic collapse and revival phenomena for quantum discord and entanglement when the field is in Fock state and the two atoms are initially in maximally mixed state, which is a special separable state. Our calculations also show that the oscillations of the time evolution of both quantum discord and entanglement are almost in phase and they both have similar evolution behavior in some time range. The fact reveals the consistency of quantum discord and entanglement in some dynamical aspects.     

General monogamy property of global quantum discord and the application

We provide a family of general monogamy inequalities for global quantum discord (GQD), which can be considered as an extension of the usual discord monogamy inequality. It can be shown that those inequalities are satisfied under the similar condition for the holding of usual monogamy relation. We find that there is an intrinsic connection among them. Furthermore, we present a different type of monogamy inequality and prove that it holds under the condition that the bipartite GQDs do not increase when tracing out some subsystems. We also study the residual GQD based on the second type of monogamy inequality. As applications of those quantities, we investigate the GQDs and residual GQD in characterizing the quantum phase transition in the transverse field Ising model.